An analogue of the Titchmarsh theorem for the Fourier transform on the group of \(p\)-adic numbers

DOI10.1134/S2070046617020066zbMath1409.11116OpenAlexW2616127698MaRDI QIDQ2403581

Sergei S. Platonov

Publication date: 11 September 2017

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s2070046617020066

zbMATH Keywords

modulus of continuityLipschitz conditiongroup of \(p\)-adic numbers\(p\)-adic Fourier transform\(p\)-adic harmonic analysisTitchmarsh theorem

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80)

Related Items (7)

Some problems in the theory of approximation of functions on the group of \(p\)-adic numbers ⋮ Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series ⋮ An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups ⋮ Characterising extended Lipschitz type conditions with moduli of continuity ⋮ Decay of Fourier Transforms and Generalized Besov Spaces ⋮ An analog of the Titchmarsh's theorem for the first Hankel-Clifford transform ⋮ Generalized \(p\)-adic Fourier transform and estimates of integral modulus of continuity in terms of this transform

Cites Work

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• Moduli of continuity of functions, defined on a zero-dimensional group
• Fourier transforms of Lipschitz functions on the hyperbolic plane \(H^2\)
• An analog of Titchmarsh's Theorem for the Dunkl transform

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